After looking to purchase a little QH and coming home with (my first) Arabian two months ago, all I have to say is that they are so intelligent, it's stupid!
I sometimes spend my lunch hour at work trying to come up with new ways to busy his mind or convince him to do something.
In my experience, they are (as was said) loyal, so very lovey, they are intelligent, they will pick up on something before it becomes conscious in your own mind... but they also demand an establishment of respect, trust and communication in a way that I have not experienced with stock breed horses. They can be spooky, or they can have [well-earned] unwavering trust in their rider. They don't always take to conventional methods of "how to," and require you to think on your feet and think creatively.
They are smart, they are fun, their endurance is breathtaking and their gaits are just so very lovely.
ETA about someone mentioning their gelding being food-driven... YES.
I have never met a horse more food-motivated than my purebred gelding!